//You are climbing a staircase. It takes n steps to reach the top. 
//
// Each time you can either climb 1 or 2 steps. In how many distinct ways can yo
//u climb to the top? 
//
// 
// Example 1: 
//
// 
//Input: n = 2
//Output: 2
//Explanation: There are two ways to climb to the top.
//1. 1 step + 1 step
//2. 2 steps
// 
//
// Example 2: 
//
// 
//Input: n = 3
//Output: 3
//Explanation: There are three ways to climb to the top.
//1. 1 step + 1 step + 1 step
//2. 1 step + 2 steps
//3. 2 steps + 1 step
// 
//
// 
// Constraints: 
//
// 
// 1 <= n <= 45 
// 
// Related Topics 动态规划 
// 👍 1643 👎 0


package leetcode.editor.cn;

//Java：Climbing Stairs
class P70ClimbingStairs {
    public static void main(String[] args) {
        Solution solution = new P70ClimbingStairs().new Solution();
        System.out.println(solution.climbStairs(4));
        // TO TEST
    }

    //leetcode submit region begin(Prohibit modification and deletion)
    class Solution {
        public int climbStairs(int n) {
            int[] memo = new int[n + 1];
            if (n == 1) {
                return 1;
            }
            if (n == 2) {
                return 2;
            }
            memo[1] = 1;
            memo[2] = 2;
            for (int i = 3; i <= n; i++) {
                memo[i] = memo[i - 1] + memo[i - 2] ;
            }
            return memo[n];
        }

        public int climbStairsC(int n) {
            memo = new int[n + 1];
            return climbStairsA(n);
        }

        int[] memo;

        public int climbStairsA(int n) {
            if (memo[n] != 0) {
                return memo[n];
            }
            if (n <= 0) {
                return 0;
            }
            if (n == 1) {
                memo[n] += 1;
                return 1;
            }
            if (n == 2) {
                memo[n] += 2;
                return 2;
            }
            return climbStairsA(n - 1) + climbStairsA(n - 2);
        }

    }
//leetcode submit region end(Prohibit modification and deletion)

}